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Commodity futures risk premiums vary across commodities and over time depending on the level of physical inventories. The convenience yield is a decreasing, non-linear function of inventories. Price measures, such as the futures basis, prior futures returns, prior spot returns, and spot price volatilities reflect the state of inventories and are informative about commodity futures risk premiums. We verify these theoretical predictions using a comprehensive dataset on 31 commodity futures and physical inventories between 1971 and 2010. While the positions of participants in futures markets vary with both returns and the state of inventories, we find no evidence that they predict risk premiums on commodity futures.